Lattice and Continuum Modelling of a Bioactive Porous Tissue Scaffold

A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient transport, and their interactions. The network structure of the physical porous scaffold is often incorporated through parameters in these models, either phenomenologically or through techniques like mathematical homogenization. We derive a model on a square grid lattice to demonstrate the importance of explicitly modelling the network structure of the porous scaffold, and compare results from this model with those from a modified continuum model from the literature. We capture two-way coupling between cell growth and fluid flow by allowing cells to block pores, and by allowing the shear stress of the fluid to affect cell growth and death. We explore a range of parameters for both models, and demonstrate quantitative and qualitative differences between predictions from each of these approaches, including spatial pattern formation and local oscillations in cell density present only in the lattice model. These differences suggest that for some parameter regimes, corresponding to specific cell types and scaffold geometries, the lattice model gives qualitatively different model predictions than typical continuum models. Our results inform model selection for bioactive porous tissue scaffolds, aiding in the development of successful tissue engineering experiments and eventually clinically successful technologies.Comment: 38 pages, 16 figures. This version includes a much-expanded introduction, and a new section on nonlinear diffusion in addition to polish throughou

Continuum Modeling and Simulation in Bone Tissue Engineering

Bone tissue engineering is currently a mature methodology from a research perspective. Moreover, modeling and simulation of involved processes and phenomena in BTE have been proved in a number of papers to be an excellent assessment tool in the stages of design and proof of concept through in-vivo or in-vitro experimentation. In this paper, a review of the most relevant contributions in modeling and simulation, in silico, in BTE applications is conducted. The most popular in silico simulations in BTE are classified into: (i) Mechanics modeling and sca old design, (ii) transport and flow modeling, and (iii) modeling of physical phenomena. The paper is restricted to the review of the numerical implementation and simulation of continuum theories applied to di erent processes in BTE, such that molecular dynamics or discrete approaches are out of the scope of the paper. Two main conclusions are drawn at the end of the paper: First, the great potential and advantages that in silico simulation o ers in BTE, and second, the need for interdisciplinary collaboration to further validate numerical models developed in BTE.Ministerio de Economía y Competitividad del Gobierno España DPI2017-82501-

CFD modeling of a fixed-bed biofilm reactor coupling hydrodynamics and biokinetics

Peer ReviewedPostprint (author's final draft

Growth behavior of human adipose tissue-derived stromal/stem cells at small scale : numerical and experimental investigations

Human adipose tissue-derived stromal/stem cells (hASCs) are a valuable source of cells for clinical applications, especially in the field of regenerative medicine. Therefore, it comes as no surprise that the interest in hASCs has greatly increased over the last decade. However, in order to use hASCs in clinically relevant numbers, in vitro expansion is required. Single-use stirred bioreactors in combination with microcarriers (MCs) have shown themselves to be suitable systems for this task. However, hASCs tend to be less robust, and thus, more shear sensitive than conventional production cell lines for therapeutic antibodies and vaccines (e.g., Chinese Hamster Ovary cells CHO, Baby Hamster Kidney cells BHK), for which these bioreactors were originally designed. Hence, the goal of this study was to investigate the influence of different shear stress levels on the growth of humane telomerase reversed transcriptase immortalized hASCs (hTERT-ASC) and aggregate formation in stirred single-use systems at the mL scale: the 125 mL (= SP100) and the 500 mL (= SP300) disposable Corning® spinner flask. Computational fluid dynamics (CFD) simulations based on an Euler⁻Euler and Euler⁻Lagrange approach were performed to predict the hydrodynamic stresses (0.06⁻0.87 Pa), the residence times (0.4⁻7.3 s), and the circulation times (1.6⁻16.6 s) of the MCs in different shear zones for different impeller speeds and the suspension criteria (Ns1u, Ns1). The numerical findings were linked to experimental data from cultivations studies to develop, for the first time, an unstructured, segregated mathematical growth model for hTERT-ASCs. While the 125 mL spinner flask with 100 mL working volume (SP100) provided up to 1.68.10⁵ hTERT-ASC/cm² (= 0.63 × 10⁶ living hTERT-ASCs/mL, EF 56) within eight days, the peak living cell density of the 500 mL spinner flask with 300 mL working volume (SP300) was 2.46 × 10⁵ hTERT-ASC/cm² (= 0.88 × 10⁶ hTERT-ASCs/mL, EF 81) and was achieved on day eight. Optimal cultivation conditions were found for Ns1u < N < Ns1, which corresponded to specific power inputs of 0.3⁻1.1 W/m³. The established growth model delivered reliable predictions for cell growth on the MCs with an accuracy of 76⁻96% for both investigated spinner flask types

Heterogeneity in pure microbial systems: experimental measurements and modeling

Cellular heterogeneity influences bioprocess performance in ways that until date are not completely elucidated. In order to account for this phenomenon in the design and operation of bioprocesses, reliable analytical and mathematical descriptions are required. We present an overview of the single cell analysis, and the mathematical modeling frameworks that have potential to be used in bioprocess control and optimization, in particular for microbial processes. In order to be suitable for bioprocess monitoring, experimental methods need to be high throughput and to require relatively short processing time. One such method used successfully under dynamic conditions is flow cytometry. Population balance and individual based models are suitable modeling options, the latter one having in particular a good potential to integrate the various data collected through experimentation. This will be highly beneficial for appropriate process design and scale up as a more rigorous approach may prevent a priori unwanted performance losses. It will also help progressing synthetic biology applications to industrial scale

Mathematical modelling of fibre-enhanced perfusion inside\ud a tissue-engineering bioreactor

We develop a simple mathematical model for forced flow of culture medium through a porous scaffold in a tissue- engineering bioreactor. Porous-walled hollow fibres penetrate the scaffold and act as additional sources of culture medium. The model, based on Darcy’s law, is used to examine the nutrient and shear-stress distributions throughout the scaffold. We consider several configurations of fibres and inlet and outlet pipes. Compared with a numerical solution of the full Navier–Stokes equations within the complex scaffold geometry, the modelling approach is cheap, and does not require knowledge of the detailed microstructure of the particular scaffold being used. The potential of this approach is demonstrated through quantification of the effect the additional flow from the fibres has on the nutrient and shear-stress distribution

A two-fluid model for tissue growth within\ud a dynamic flow environment

We study the growth of a tissue construct in a perfusion bioreactor, focussing on its response to the mechanical environment. The bioreactor system is modelled as a two-dimensional channel containing a tissue construct through which a flow of culture medium is driven. We employ a multiphase formulation of the type presented by G. Lemon, J. King, H. Byrne, O. Jensen and K. Shakesheff in their study (Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol. 52(2), 2006, 571–594) restricted to two interacting fluid phases, representing a cell population (and attendant extracellular matrix) and a culture medium, and employ the simplifying limit of large interphase viscous drag after S. Franks in her study (Mathematical Modelling of Tumour Growth and Stability. Ph.D. Thesis, University of Nottingham, UK, 2002) and S. Franks and J. King in their study (Interactions between a uniformly proliferating tumour and its surrounding: Uniform material properties. Math. Med. Biol. 20, 2003, 47–89).\ud \ud The novel aspects of this study are: (i) the investigation of the effect of an imposed flow on the growth of the tissue construct, and (ii) the inclusion of a mechanotransduction mechanism regulating the response of the cells to the local mechanical environment. Specifically, we consider the response of the cells to their local density and the culture medium pressure. As such, this study forms the first step towards a general multiphase formulation that incorporates the effect of mechanotransduction on the growth and morphology of a tissue construct. The model is analysed using analytic and numerical techniques, the results of which illustrate the potential use of the model to predict the dominant regulatory stimuli in a cell population

Introducing monitoring and automation in cartilage tissue engineering, toward controlled clinical translation

The clinical application of tissue engineered products requires to be tightly connected with the possibility to control the process, assess graft quality and define suitable release criteria for implantation. The aim of this work is to establish techniques to standardize and control the in vitro engineering of cartilage grafts. The work is organized in three sub-projects: first a method to predict cell proliferation capacity was studied, then an in line technique to monitor the draft during in vitro culture was developed and, finally, a culture system for the reproducible production of engineered cartilage was designed and validated. Real-time measurements of human chondrocyte heat production during in vitro proliferation. Isothermal microcalorimetry (IMC) is an on-line, non-destructive and high resolution technique. In this project we aimed to verify the possibility to apply IMC to monitor the metabolic activity of primary human articular chondrocytes (HAC) during their in vitro proliferation. Indeed, currently, many clinically available cell therapy products for the repair of cartilage lesions involve a process of in vitro cell expansion. Establishing a model system able to predict the efficiency of this lengthy, labor-intensive, and challenging to standardize step could have a great potential impact on the manufacturing process. In this study an optimized experimental set up was first established, to reproducible acquire heat flow data; then it was demonstrated that the HAC proliferation within the IMC-based model was similar to proliferation under standard culture conditions, verifying its relevance for simulating the typical cell culture application. Finally, based on the results from 12 independent donors, the possible predictive potential of this technique was assessed. Online monitoring of oxygen as a non-destructive method to quantify cells in engineered 3D tissue constructs. This project aimed at assessing a technique to monitor graft quality during production and/or at release. A quantitative method to monitor the cells number in a 3D construct, based on the on-line measurement of the oxygen consumption in a perfusion based bioreactor system was developed. Oxygen levels dissolved in the medium were monitored on line, by two chemo-optic flow-through micro-oxygen sensors connected at the inlet and the outlet of the bioreactor scaffold chamber. A destructive DNA assay served to quantify the number of cells at the end of the culture. Thus the oxygen consumption per cell could be calculated as the oxygen drop across the perfused constructs at the end of the culture period and the number of cells quantified by DNA. The method developed would allow to non-invasively monitoring in real time the number of chondrocytes on the scaffold. Bioreactor based engineering of large-scale human cartilage grafts for joint resurfacing. The aim of this project was to upscale the size of engineered human cartilage grafts. The main aim of this project consisted in the design and prototyping of a direct perfusion bioreactor system, based on fluidodynamic models (realized in collaboration with the Institute for Bioengineering of Catalonia, Spain), able to guarantee homogeneous seeding and culture conditions trough the entire scaffold surface. The system was then validated and the capability to reproducibly support the process of tissue development was tested by histological, biochemical and biomechanical assays. Within the same project the automation of the designed scaled up bioreactor system, thought as a stand alone system, was proposed. A prototype was realized in collaboration with Applikon Biotechnology BV, The Netherlands. The developed system allows to achieve within a closed environment both cell seeding and culture, controlling some important environmental parameters (e.g. temperature, CO2 and O2 tension), coordinating the medium flow and tracking culture development. The system represents a relevant step toward process automation in tissue engineering and, as previously discussed, enhancing the automation level is an important requirement in order to move towards standardized protocols of graft generation for the clinical practice. These techniques will be critical towards a controlled and standardized procedure for clinical implementation of tissue engineering products and will provide the basis for controlled in vitro studies on cartilage development. Indeed the resulting methods have already been integrated in a streamlined, controlled, bioreactor based protocol for the in vitro production of up scaled engineered cartilage drafts. Moreover the techniques described will serve as the foundation for a recently approved Collaborative Project funded by the European Union, having the goal to produce cartilage tissue grafts. In order to reach this goal the research based technologies and processes described in this dissertation will be adapted for GMP compliance and conformance to regulatory guidelines for the production of engineered tissues for clinical use, which will be tested in a clinical trial

Controlled diffusion processes with markovian switchings for modeling dynamical engineering systems

A modeling approach to treat noisy engineering systems is presented. We deal with controlled systems that evolve in a continuous-time over finite time intervals, but also in continuous interaction with environments of intrinsic variability. We face the complexity of these systems by introducing a methodology based on Stochastic Differential Equations (SDE) models. We focus on specific type of complexity derived from unpredictable abrupt and/or structural changes. In this paper an approach based on controlled Stochastic Differential Equations with Markovian Switchings (SDEMS) is proposed. Technical conditions for the existence and uniqueness of the solution of these models are provided. We treat with nonlinear SDEMS that does not have closed solutions. Then, a numerical approximation to the exact solution based on the Euler- Maruyama Method (EM) is proposed. Convergence in strong sense and stability are provided. Promising applications for selected industrial biochemical systems are showed